The goal of this proposal is to develop statistical methods for the analysis of failure time data that involve missing prognostic factors, complicated ascertainment, and/or dependencies. The Specific Aims are motivated by problems arising in natural history clinical studies of brain tumors and laboratory studies of the molecular biology of brain tumors and by studies of familial aggregation of multiple cancers. Empirical data analysis will play a central role in each of the Specific Aims. Brain tumors typically have histological diagnoses that are only weakly associated with prognosis and genetic features that are only partially known. The impact of the resultant unexplained heterogeneity will be investigated for a general class of failure time models. Adaptive designs to remedy the resultant loss of power will be proposed. The known heterogeneity of brain tumors, and the resultant small numbers of subjects with a given diagnosis, frequently precludes large prospective studies. This leads to the use of natural history studies, and introduces delayed entry (truncation). Tests of independence of truncation and failure for a variety of situations will be derived and evaluated, and methods that appropriately adjust for dependence will be developed. Familial aggregation studies are characterized by dependencies among and within family members and by complex ascertainment schemes. Computationally simple methods will be developed for analysis of scientific quantities of interest, i.e., conditional and partially marginal measures of response and association that retain interpretability with families of varying sizes. Extensions to ordinal and censored data will be derived. Software will be developed, and made freely available, for optimal family study design, allowing for multiple disease outcomes and complex, non-random ascertainment. [unreadable] [unreadable]